Gradient trust region algorithm with limited memory BFGS update for nonsmooth convex minimization

By means of a gradient strategy, the Moreau‐Yosida regularization, limited memory BFGS update, and proximal method, we propose a trust‐region method for nonsmooth convex minimization. The search direction is the combination of the gradient direction and the trust‐region direction. The global convergence of this method is established under suitable conditions. Numerical results show that this method is competitive to other two methods.